The design of filters with lumped elements is a well advanced art. Darlington (J. Math. Phys., 18, 257-353, Sept. 1939) has shown how the elements of a filter may be found for a prescribed transmission versus frequency (power transmission ratio) subject to certain constraints so as to make the filter physically realizable with passive elements. A power ratio with prescribed maximum excursions within the passband is conveniently represented by a Tchebysheff polynomial of the first kind. There are many other filter types that realize given transmission characteristics (Zverev, Handbook of Filter Synthesis, John Wiley and Sons, 1967). Tchebysheff filters have been realized with microwave cavities by utilizing their lumped circuit representation (Microwave Transmission Circuits, McGraw Hill Book Co., Inc., 1948).
Surface Acoustic Wave (s.a.w.) resonators have been realized recently with very high Q's (Li, R. C. M., J. A. Alusow, and R. C. Williamson, 1975 Ultrasonics Symposium Proceedings, IEEE Cat. No. 75 CHO 994-4SO, 279-283, 1975). Identical resonators have been cascaded so as to realize a filter design with a (relatively) flat passband and steep falloffs into the cutoff bands (Haus, H. A., and R. V. Schmidt, IEEE Trans. On Sonics and Ultrasonics, V. SU-24, No. 2, March 1977). However, the preceding paper did not disclose the criteria for realizing specific filter designs with s.a.w. resonators.